Real-Life Problem Solving with Equations
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Real-Life Problem Solving with Equations — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionChoosing Appropriate MethodsConcept Practice
4 marks~6 minCriterion A
A cyclist's journey is modelled by a straight-line graph of distance (km) against time (hours). The line passes through the points (1,15)(1, 15) and (3,45)(3, 45).
a
Calculate the cyclist's speed. [1]
b
Deduce the equation of the line in the form d=mtd = mt, where dd is distance in km and tt is time in hours. [1]
c
The cyclist's destination is 70 km away. Using your equation, advise whether the cyclist should plan to complete the journey within a 5-hour window. Justify your answer. [2]
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Solutions

2QuestionMulti-Step Problems with VariablesAssessment Practice
4 marks~6 minCriterion D
A solar panel installation company charges a connection fee plus a fixed rate per panel installed. The graph shows total cost yy (dollars) against number of panels xx, passing through (0, 50)(0,\ 50) and (10, 200)(10,\ 200).
a
Calculate the rate charged per panel. [1]
b
Deduce the equation of the line in the form y=mx+cy = mx + c. [1]
c
A community centre has a budget of 420 dollars for this installation. Advise the centre manager whether the budget is sufficient for 25 panels, justifying your answer with a calculation. [2]
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Solutions

3QuestionMulti-Step Problems with VariablesConcept Practice
2 marks~3 minCriterion B
A community centre arranges daily volunteer shifts. The shift lengths (in hours) follow a pattern of consecutive integers:

Day 1: 1+2=31 + 2 = 3 hours
Day 2: 2+3+4=92 + 3 + 4 = 9 hours
Day 3: 3+4+5+6=183 + 4 + 5 + 6 = 18 hours
Day 4: 4+5+6+7+8=304 + 5 + 6 + 7 + 8 = 30 hours

On Day 5, shifts run for 6 consecutive integers starting at 5.
a
Deduce the pattern connecting the sum of each set to its terms. [1]
b
A volunteer coordinator claims Day 5 totals exactly 45 hours of coverage. Justify whether this claim is correct. [1]

Solutions

4QuestionInterpreting and Validating SolutionsConcept Practice
2 marks~3 minCriterion C
A mobile data plan charges a monthly fee. Plan A costs 4x−74x - 7 dollars and Plan B costs 2x+52x + 5 dollars, where xx is the number of gigabytes used.

A customer claims that both plans cost the same when x=6x = 6 gigabytes.

Substitute x=6x = 6 into both expressions, show your working, and justify whether the customer's claim is correct. [2]

Solutions

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